Effect of Tax Changes on TFP: An Empirical and Theoretical Analysis.∗ Syed Muhammad Hussain† November 15, 2011

Abstract I analyze the effects of tax policy changes on US total factor productivity (TFP). Data on tax shocks comes from the sources used by Romer and Romer (2009). VAR estimates show that a 1 percent permanent exogenous rise in total taxes lowers TFP by up to 1.75 percent in the long run. Individual income taxes have a strong and significant effect on TFP whereas corporate income taxes do not significantly affect TFP. I then build a DSGE model which has learning by doing at the worker level and endogenous TFP evolution that depends on investment and human capital. When I calibrate the learning-by-doing and TFP evolution processes as in the literature, the effect of taxes on TFP in the model is substantially less elastic than in the data. I argue that this difference may arise because tax changes labeled as exogenous by Romer and Romer can give spurious results or because of a mis-specified model.

JEL Classification: H31, H32, O41, O47, O51. Key Words: TFP, Taxes, VAR, DSGE, Learning by doing, Endogenous Growth.

∗ I would like to thank Ryan Michaels, William Hawkins, and Mark Bils for advising me during this paper and providing me with valuable feedback and comments. All mistakes are my own. † Department of Economics, Harkness Hall, University of Rochester, Rochester, NY, 14627,USA. Email: [email protected]

1

1

Introduction

TFP, defined as the amount of output not explained by inputs used, is an important determinant of long run growth of an economy. TFP growth, in turn, is the culmination of investments in ideas and technologies, as stressed by recent work in new growth theory.1 Given this endogenous nature of TFP, one would expect public policy to affect the path of TFP through its effect on the relative price of investment. Yet there have been no attempts to estimate the dynamic response of TFP to policy changes. This paper seeks to fill this gap by looking at the post war US economy to quantify the effects of tax changes on TFP.

The empirical part of the paper estimates the effect of increasing taxes on TFP. There are two main results. First, TFP shows a strong, significant, and negative response to this policy change in the long run. This represents about 80 percent of the change in real output due to the policy change. Second, even in the short run, changes in TFP account for about one third of the response of output. Further, the results show that only changes in labor income taxes have a significant impact on TFP and other macroeconomic variables while changes in capital income taxes do not significantly affect most of the variables.

I use the vector autoregressive (VAR) technique to do the empirical analysis. For the TFP measure, I use the measure of Basu et al. (2006) who purify the Solow residual by controlling for unobserved variations in utilization of inputs. I obtain the measure of tax changes by pooling data on all ”exogenous” tax changes documented by Romer and Romer (2009). They classify a tax change as exogenous if the narrative records of the time reveal that the tax policy change was not motivated by current economic conditions. I use this sub-sample in my baseline analysis to guard against possible reverse causality: a negative TFP shocks may lead to a recession and output contraction which would in turn motivate an “endogenous” tax cut to bring output back to normal. I also use the same data sources as Romer and Romer (2009), but refine their methodology to identify separately changes in personal and corporate income tax liabilities and look at the effect of these two types of tax shocks on various macroeconomic variables. I also subject the empirical findings to a series of robustness checks. The results are robust to various changes in measures of taxes and TFP.

The second part of the paper asks whether the large estimated effects on TFP of taxes can be consistent with standard macroeconomic models. Many macroeconomic models of the business cycle, for example the real business cycle model (Kydland and Prescott (1982), Long and Plosser (1983)) and the New Keynesian model (Christiano et al. (2005)), do not endogenize TFP, and so cannot be used to analyze the response 1 See Ribeiro (2003) and Acemoglu (2008) for a comprehensive review of endogenous growth models and the various mechanisms they employ.

2

of TFP to policy changes. One leading class of candidate models in which TFP is endogenous is the class of new growth models (Romer (1990), Lucas (1988)); however, it seems unlikely that innovation is important for driving fluctuations in TFP. A leading possible explanation that could potentially account for movements in TFP following a tax change is a model in which learning-by-doing takes the form of an externality: the TFP of all firms is increased when human capital is high. Therefore I build a DSGE model with this feature, and ask whether it can be consistent with the empirical responses of TFP to tax policy changes.

The simulations of the model show that for carefully chosen parameter values of the model, the model generated dynamic responses of various variables to tax shocks are qualitatively consistent with their empirical counter parts. However, in quantitative terms, these model generated responses fall short of the empirical estimates. In particular, the drop in TFP in the model is only about one fourth of the values obtained from the empirical exercise. The model is successful in matching the differential effects of labor and capital taxes observed in the data. This asymmetry comes from the difference in magnitudes of elasticities of TFP with respect to investment and human capital. In particular, a higher elasticity of TFP with respect to human capital and a low elasticity of TFP with respect to investment leads to this result. Labor income taxes reduce hours and consequently the experience of the workers. This effect is then transmitted to other variables in the economy through the TFP channel. Similarly capital income taxes have their effect felt via TFP as well. Since the TFP elasticity of human capital is bigger, the effects resulting from labor income taxes are also bigger quantitatively. I then re-estimate the model without imposing any restrictions on the parameters. The results show that the model is able to closely match the empirical results in this case.

I argue that the gap between the empirical and model generated results can be either because the data overstates the true impact of changes on TFP, or because of the model missing an important channel, or because the parameter values are underestimated by micro studies as they may miss some of the macro effects. If these underestimated values are used in the model the model will fall short of the empirical estimates.

This paper is the first to look at the effects of tax changes on TFP. Heylen and Schoonackers (2011) use data on OECD countries from 1975 to study the effect of taxes and other fiscal variables on labor productivity (output per hour). They find that a rise in personal income taxes significantly reduces the labor productivity. At a micro level, Gemmel et al. (2010) and Arnold and Schwellnus (2008) use a panel data of firms of OECD countries over the period 1996-2004 to show that raising corporate taxes reduce the productivity of firm by 0.2 to 0.4 percent. Kim (1998) used an endogenous growth model to explain that difference in tax rates explain about 30 percent of the difference in growth rates of the USA and Korea. 3

This paper contributes to the existing literature on the macroeconomic effects of tax shocks such as Mertens and Ravn (2011), Romer and Romer (2010), Blanchard and Perotti (2002), and McGrattan (1994). These papers look at the response of various macroeconomic variables (not including TFP) to tax shocks. Mertens and Ravn (2011) also showed that a DSGE model is capable of replicating empirical responses of macroeconomic variables to tax shocks as identified by Romer and Romer (2009). None of these papers look at the possible effects of tax shocks on TFP which can have important effects since effects on TFP translate into long term growth effects of the economy. This paper attempts to fill this void by using the data of Romer and Romer (2009) about tax shocks with TFP estimates by Fernald (2009) to empirically estimate the response of TFP to tax shocks.

The rest of the paper is structured as follows: Section 2 describes the data and section 3 describes the empirical specification, results and various robustness checks. Section 4 describes the model and its simulation results. Section 5 discuses the empirical and model results. Section 6 concludes the paper.

2

Data

The data on tax shocks comes from Romer and Romer (2009). Romer and Romer (2009) study each major tax bill signed in the post war era in the United States. They classify each tax change as either exogenous or endogenous based on their analysis of government documents, presidential speeches and congressional documents. Tax changes undertaken in response to concerns about inherited debt or the changes motivated by long term growth are classified as exogenous. Tax changes that were made in response to spending incidents or to bring back output to normal are classified as endogenous.2 The measure of tax shocks used in their study is the changes in tax liabilities resulting from each tax bill. The study covers the period 1947Q1 to 2007Q4. In all, there are 67 quarters with non-zero tax liability changes. Out of these, 44 quarters have changes in tax liability which result from exogenous tax shocks and in 41 of those quarters, changes are from permanent tax shocks.

Romer and Romer (2009) give a change in total tax liability resulting from major tax bills. I use the sources used in their study to document the changes in tax liability resulting from changes in personal and corporate taxes. Where the sources of Romer and Romer (2009) do not give the changes in personal and cor2 The most obvious example of a tax change made in response to spending incidents would be a tax increase in the event of a war. A war causes the spending of the government to go up which is then financed by a increase in taxes. Since such a tax increase is made in response to a contemporaneous activity in the economy, it is classified as endogenous.

4

porate taxes, I use similar sources to documents these changes. There are 58 quarters where personal taxes change and in 37 of these quarters, the changes are exogenous and all of these are permanent. There are 46 quarters with changes in corporate taxes. 34 of these have exogenous changes and 32 of them are permanent.

Romer and Romer (2010) divide their series of changes in total tax liabilities by the nominal gdp to form their tax measure of changes in percentage points of tax to gdp ratio. Following their approach, I divide the changes in personal tax liabilities by personal income and I divide the changes in corporate tax liabilities by corporate profits.3 For the benchmark case, I use the exogenous permanent changes in taxes as measure of tax shocks. Figure (1) shows these tax series.

The data on TFP comes from Fernald (2009). He uses the methodology used in Basu et al. (2006) on quarterly data to estimate a TFP series from 1947Q1-2007Q4. Basu et al. (2006) construct a TFP series which is corrected for variable capital and labor utilization. For this, they use change in hours worked as proxy for both labor and capital utilization. They estimate a estimate a purified version of TFP at an industry level and then aggregate it using industry’s share of aggregate nominal value added.4

The data on output, investment, and consumption comes from Bureau of Economics Analysis (BEA). All three variables are measured using chain-type quantity index. The data on labor hours and employment comes from the Bureau of Labor Statistics (BLS). I use hours in non-farm business sector from the labor productivity and costs database of the BLS. All the variables are in per capita terms. The data on population also comes from the BLS.5 Table (1) gives a summary of data sources used for this paper.

3

Empirical Specification

Following Romer and Romer (2010), in the benchmark case, I estimate a three variable VAR with 12 lags to find the impact of tax shocks on TFP.

Xt = A + B(L)Xt−1 + t

(1)

3 This is a way to put all the tax changes on a consistent basis. In this way these tax changes can roughly be thought of changes in percentage points of average tax rates. 4 For details see Basu et al. (2006). 5 Data on population is available from 1948 onwards so for variables that are converted to per capita terms, the analysis is from 1948Q1-200Q4. Since there were no non-zero observation in the data for tax shocks for the year 1947, this does not change the results at all.

5

where B(L) is a p-order lag polynomial, t is the vector of shocks and Xt = [xt , yt , τt ]0 . xt is the log of TFP, yt is the log of output and τt is the tax measure described above. The key assumption in this analysis is that the changes in taxes are observable and exogenous. Although Romer and Romer (2010) classify tax changes as either endogenous or exogenous, there still may be an element of doubt that there is some endogeneity in the ”exogenous” tax changes as well. Mertens and Ravn (2011) formally test this assumption and find that past values of exogenous tax shocks have no predictive power for future exogenous tax changes. In contrast they find that past values of endogenous tax changes have predictive power for future tax changes.

I also estimate equation (1) with personal and corporate taxes in place of total taxes. In doing so, I assume that the changes in personal and corporate taxes corresponding to total tax changes deemed exogenous by Romer and Romer (2010) are exogenous as well.

3.1

Results

Figure (2) reports the impulse response of TFP to a 1 percentage point rise in the relevant tax measure along with one standard error bands.67 The impulse responses are calculated for 20 quarters. Panel (a) in Figure (2) shows that TFP shows no change on impact before steadily falling for the next several quarters. The maximum drop in TFP is of 1.75 percent and that occurs after 14 quarters. TFP then starts to rise again albeit very slowly. The overall impulse response of TFP shows that it falls permanently, or nearly so, in response to a one percent rise in taxes. Another way to state this result is that tax reductions lead to permanent increases in the level of TFP.

Panel (b) of Figure (2) shows the response of TFP to a 1 percent rise in personal income taxes. The figure shows that the effect on TFP in the first few quarters of change is small and insignificant. TFP then falls for the next few quarters. The maximum fall occurs after 14 quarters when TFP drops by 1.52 percent. The fall in TFP again seems to be permanent. Panel (c) shows the impulse response of TFP to a 1 percent rise in corporate taxes. In this case TFP does not show any significant change in response to a one percentage point rise in the corporate tax measure. Even the point estimates do not show any regular trend. Thus Figure (2) shows that a one percentage point rise in tax revenue to GDP ratio reduces TFP significantly and permanently. An innovation in individual taxes has a similar effect whereas corporate taxes do not affect TFP.

6 For total taxes, this changes implies a tax increase of one percent of GDP, for individual taxes, this implies a tax increase of one percent of total personal income, and for corporate profits, it implies a tax increase of one percent of total pre tax corporate profits. 7 The standard errors reported in these graphs are the stata calculated asymptotic standard errors.

6

Figure (3) show the response of TFP and real output to 1 percent rise in total tax liabilities. It shows that in the short run the changes in TFP account for about one third of the movement in output following a tax shock. In the long run the response of output and TFP become closer which shows that in the long run TFP is responsible for a large part of the change in output. Thus, when investigating the impact of tax changes in a business cycle environment, it is important to treat TFP as an endogenous variable that can be affected by tax changes.

3.1.1

Other Measures of Taxes

As mentioned earlier, in the benchmark case, I only considered those tax changes that were deemed exogenous by Romer and Romer (2009). However, it can be argued that the tax changes classified as endogenous in their work are also exogenous for the purpose of this paper since it is unlikely that the endogenous tax changes were made in response to movements in TFP. For this reason, I estimate equation (1) again, this time including both exogenous and endogenous tax changes.8 The results are in Figure (4) . A one percentage point increase in the total tax revenue to GDP ratio initially had no effect on TFP. TFP then starts to falls but the fall is slower than in the case with only exogenous tax changes. The maximum drop in TFP is of 1.37 percent and it takes place 16 quarters after the innovation in the tax process. Thus the effect on TFP of tax shocks appears to be both slower and smaller when endogenous tax changes are considered. Panel (b) of Figure (4) shows that when endogenous personal tax changes are considered, the effect on TFP is quicker and smaller compared to the case when only exogenous changes are considered. The maximum drop in this case is of 1.1 percent and it occurs after 7 quarters of the initial shocks. The overall impact nonetheless is permanent like in the case of exogenous shocks although the magnitude is slightly smaller. Panel (c) shows that corporate tax changes still don’t show any systematic effect on TFP; the point estimates are close to zero and highly insignificant. Thus including endogenous tax changes in the tax measures does not affect the results much: the effect of total and personal taxes is till negative, insignificant and permanent and that of corporate taxes on TFP is small and insignificant.

I also consider the response of TFP to a change in effective average tax rates. It is unlikely that the movements in these tax rates are completely exogenous to TFP. The movements in tax rates are correlated with output and other factors that affect TFP directly. Inclusion of output in the VAR structure will address this problem to some extent but will not make the average tax rates completely exogenous to TFP. I, 8 I exclude the tax changes that were taken in response to the war time expenditures that took place during the Korean War. Romer and Romer (2010) show that the tax changes taken in response to Korean war are outliers in the data which push the results closer to zero. If these changes are also included then the long run response of TFP goes down numerically but remains strong. The maximum drop in that case is of 0.96 percent. The short run response remain very similar.

7

nonetheless, estimate equation (1) with these tax rates.

There are no readily available measures of average tax rates. To calculate these, I use the methodology of Mendoza et al. (1994). Specifically, I consider average labor and capital tax rates. These are given by

τL =

τK =

τI W + tss + tpay W + tssemp

τI (OSP U E + P EI) + tcorp + tprop + ttrans OS

where τI is the income tax given by

τI =

tpers OSP U E + P EI + W

In these formulae, • tpers - Taxes on incomes, profits, and capital gains of individuals. • tcorp - Taxes on incomes, profits, and capital gains of corporations. • tss - Social Security contributions. • tssemp - Social Security contributions of employers. • tpay - Taxes on payroll and workforce. • tprop - Recurrent taxes on immovable property. • ttrans - Taxes on financial and capital transactions. • OSPUE - Operating surplus of private unincorporated enterprises. • OS - Operating surplus of the economy. • PEI - Household property and entrepreneurial income. • W - Wages and salaries. Mendoza et al. (1994) use OECD data for their calculations. OECD data, however, is not available at quarterly frequency. I use Bureau of Economic Analysis data instead. The results of using this tax measure in equation (1) are in figure (5). The first panel shows that in response to a one percent rise in the marginal labor tax rate, TFP starts to drop immediately. The drop becomes significant after 7 quarters at which

8

point the drop is of 1.2 percent. TFP then does not recover and the value remains around 1 percent in the long run. Panel (b) repeats the exercise for capital tax rates.9 The plot shows that TFP does not show any response to changes in marginal capital tax rates.

3.1.2

Other Measures of TFP

So far, the measure of TFP that has been used in this paper is the utilization adjusted TFP as calculated by Fernald (2009). In this section, I consider two other measures of TFP. The first is unadjusted TFP, which is defined as value added per combined unit of labor and capital input. The Bureau of Labor Statistics reports this measure of TFP annually for major sectors and then aggregates. Fernald (2009) estimates a similar series at a quarterly frequency and shows that his estimated series is almost identical to the series estimated by BLS. I use Fernald’s (2009) series in this section.10

I estimate equation (1) for this measure of TFP. I used changes in total tax revenues that are exogenous. I also estimate it for individual and corporate taxes. The results are in figure (6). Again the response of utilization adjusted TFP from the previous subsection is plotted for comparison. The first panel of this figure shows that unadjusted TFP responds much more sharply to changes in total taxes. It shows no significant response in the first 3 quarters and then falls sharply. The maximum drop in unadjusted TFP is 2.17 percent after 7 quarters. It then starts to rebound slowly. A comparison with the response of utilization adjusted TFP shows that the drop in unadjusted TFP is both faster and larger. The drop in utilization adjusted TFP after 7 quarters is only 0.73 percent. Furthermore, the drop in unadjusted TFP is lower than the drop in utilization adjusted TFP in the long run. These results suggest that since utilization of labor and capital is the difference between these two measures of TFP, it must be the case that utilization falls sharply on impact before recovering slightly.11 Thus to sum up this result, unadjusted TFP shows a sharp negative response in the short run while utilization adjusted TFP shows a strong negative response in the long run. This result also suggests that utilization adjusted TFP is a better measure of overall productivity since productivity, unlike other inputs like capital and labor, should not change immediately to a change in taxes. Panel (b) shows the response of these two measures of TFP to a shock to individual taxes. It shows the same result the unadjusted TFP drops in the short run before rebounding in the long run while utilization adjusted TFP shows no response in the short run. Panel (c) shows that unadjusted TFP does not show any response to 9 Mendoza

et al. (1994) do no give a formula to calculate corporate tax rates. I calculated average corporate tax rates by dividing the taxes paid by corporation by the total pre tax incomes of corporations. Panel (c) shows the result of using this tax measure. 10 Fernald (2009) then cleans this series of utilization to arrive at the purified measure of TFP that was used in the previous subsection. 11 Later in the paper, I look at the effect of tax shocks on hours per person in the economy, the results indeed show that hours fall for the first few quarters in response to a ta shock and then rise. The effects are insignificant though.

9

changes in corporate taxes just like utilization adjusted TFP.

The other measure of TFP that I use comes from Bils and Cho (1994). They consider a production function of the following form 0 1−α Yt = Zt Lα t (Kt )

where Lt = φt Ht Nt

Kt0 = (φt Ht )µ Kt where φt is the level of effort exerted by workers. In this specification, it is assumed that capital utilization and labor effort increase with longer work hours and higher effort exerted. Intuitively, the Bils and Cho (1994) methodology of measuring utilization is the same as that of Basu et al. (2006) i.e. both capital utilization and worker effort depend on hours worked. However, Bils and Cho (1994) used existing studies to calibrate the output elasticity of hours to incorporate this utilization at capital and worker level instead of estimating it like Basu et al. (2006).12

I estimate equation (1) for this measure of TFP and the results are in figure (7). The first panel shows the response of Bils and Cho measure of TFP (with µ = 0.64 which implies constant effort and capital utilization) to a percent rise in tax revenues to GDP ratio. The maximum drop in this case is of 1.21 percent and that occurs after 7 quarters. The response of this measure of TFP from Bils and Cho (1994) closely resembles the response of unadjusted TFP which is not surprising since utilization of capital and labor have not been taken into account. The second panel plot the response of Bils and Cho measure for µ = 1 which implies procyclical utilization of capital but no change in worker effort. The result in this case is very similar to the first one. The maximum drop of 1.12 percent again takes place after 7 quarters. The long run response in this case is stronger than the case with constant worker effort and capital utilization. The third panel shows the response of third measure of Bils and Cho in which µ is set to 1.5 which corresponds to the case 12 Bils and Cho (1994) study the relationship between the workweek of loom in the U.S. Textile sector and hours per worker in the same sector and find that the elasticity of loom hours with respect to hours per worker is about 0.9. To further examine this, they examine the relationship between electricity consumption and hours worked and find that the elasticity of electricity consumption with respect to hours is about 1.2. Based on these, they conclude that capital utilization increases proportionately with hours worked. For the relationship between worker effort and hours worked, they use the study of Schor (1988) on British Manufacturing for the years 1970-1986 and conclude that elasticity worker effort with respect to workweek is 0.5. The eventual production function (Yt = Zt Ntα Htµ (Kt )1−α ) uses 3 different elasticities of output with respect to hours. I use the US quarterly data to calculate TFP (Z) in the above production function. To calculate capital stock, I use the perpetual inventory method with a discount factor of 0.025.

10

where both worker effort and capital utilization vary proportional to the work week. The response of this measure of TFP is very close, both qualitatively and quantitatively, to that of the baseline measure of TFP. Unlike the first two measures which both decline in the short run before rising again, this measure of Bils and Cho (1994) TFP shows a steady decline just and the baseline measure of TFP. The maximum drop of 1.17 percent occurs after 20 quarters.

3.1.3

Changes Over Time

Figure (8) reports the estimates equation (1) separately for the pre and post 1980 periods. This exercise is done to check whether the effect of taxes on TFP has remained constant over time or not. The results are striking. The plot shows that taxes have no effect on TFP in the pre 1980 period whereas they have a strong effect on TFP in the post 1980 period. In the pre 1980 period, increases in corporate taxes seem to have a positive effect on TFP in the short run. Furthermore, the estimates for the post 1980 period are very precise. This shows that the effects of taxes have become stronger, more significant and more negative over time. If the tax series were significantly different in the two time periods, it could explain some part of this difference. However, the tax series seem to have the same properties in the two time periods. There are 24 tax changes in the pre 1980 period and 17 in the post which imply one tax change every 6 quarters on average. The size of tax changes in these two periods are different however. Average change in tax revenue to GDP ratio in the pre 1980 period is .04 percent whereas that in the post 1980 period is .02 percent. The exact reason for this change in response of TFP to changes in taxes is left as a future research question.

3.1.4

Effect of Taxes on other Macroeconomic Variables

In this section, I look at the effect of tax shocks on various macroeconomic variables other than TFP. For output, I estimate a 2 variable VAR containing the log of output and the tax measure, while for all other variables I estimate a 3 variable VAR (equation (1))using log of the relevant variable, log of output and the tax measure.13 I use the exogenous tax shocks as my measure of tax changes in all cases.

The first panel of Figure (9) shows the effect of a one percentage point increase in the ratio of ta revenue to GDP on output. The plot shows that there is no significant effect on output upon impact and then it starts to drop slowly. The drop in output becomes significant after 5 quarters. Output then starts to increase slightly but does not return to its original value even in the long run. Thus tax shocks have a permanent negative impact on output. Panel (b) of the same figure shows that individual taxes have a 13 For variables expressed in per capita terms like investment, capital, consumption etc., I use output per capita instead of total output in the VAR. The results change very little if total output is included instead.

11

similar impact on output. Panel (c) shows that corporate taxes do not have any significant impact on output.

Figure (10) reports the result from estimating equation (1) for gross private investment. The first two panels show that total and individual taxes have strong negative effects on investment. In both cases the maximum drop takes place after 7 quarters. The third panel shows that corporate taxes have some negative effect on investment in the short but this effects disappears quickly. Figure (11) shows that all three types of taxes have a significant, permanent and negative impact on the capital stock.14 Corporate taxes have smaller impact as compared to the impact that total and individual taxes have.

Figure (12) shows the response of average hours worked in the non farm business sector. The data for average hours worked comes from the Bureau of Labor Statistics.15 None of the taxes seem to have any significant impact on average hours worked. The point estimates show that in response to all three types of taxes, hours first go down before increasing in the long run. This also confirms the earlier discussion regarding utilization. Since hours worked are used to estimate utilization, and since hours worked seem to drop in the short run before rising in the long run, utilization also behaves in the same way which is consistent with the responses of unadjusted and utilization adjusted TFP. Figure (13) shows the response of total employment to tax shocks. The results show that employment drops in the short run in response to tax shocks but starts to rebounds back after about 8 quarters. The drop in the case of total and individual taxes is between 1 and 1.5 percent whereas the drop is around 0.2 percent in response to corporate tax shocks. Thus these results show that in response to tax shocks, average hours worked move little but total employment falls in the short run.

Figure (14) shows the response of output per hour to tax shocks. Output per hour drops significantly in the short run in response to all three types of shocks before rebounding. However the effect on output per hour of tax shocks appears to be permanent in the long run although the estimates are not very precise. Figure (15) shows that real wage does not respond to changes in total or individual taxes but it drops significantly in response to corporate taxes. Furthermore, this drop seems to be permanent. Finally, Figure (16) shows the response of private consumption to tax shocks. It shows that consumption falls in response to total and individual taxes although in case of individual taxes the estimates are not very precise. In response to corporate taxes, consumption falls for about 5 quarters before going back to its original value. 14 Capital

stock was constructed using the perpetual inventory method with a depreciation rate of 0.025. series for average hours is constructed by dividing total hours (from the BLS) by the total adult population (also from the BLS). 15 The

12

3.2

Comparison to Existing Literature

The results of this section have showed that total tax shocks have strong and significant negative effects on TFP. The results have also showed that only changes in personal income taxes affect TFP and other variables significantly, while corporate taxes have no significant effect on most of the variables.

This is the first paper that looks at the effect of tax changes on TFP. Other studies have looked at the effects of taxes on either growth rates or labor productivity. Heylen and Schoonackers (2011), looking at a panel data of OECD countries from 1975-2007, find that personal income taxes have a significant negative effect on labor productivity.16 However, their methodology differs from the empirical strategy adopted in this paper in two ways. First, their analysis is essentially static, that is, they do not look at the possible effects that taxes may have in future periods. Second, they study the effect of taxes on labor productivity rather than on multifactor productivity (TFP). They also do not control for unobserved utilization of inputs.

Other studies have looked at the impact of taxes on growth of output. Kneller et al. (1999) use panel data on 22 OECD countries over the period 1970-1995 and find that distortionary taxes17 have significantly negative effects on per capita growth of GDP. Barro and Redlick (2009) find that average marginal income tax rates have strong negative effects on real GDP growth in the post war US economy. Blankenau (2007) use panel data on 23 developed countries for the 1960-2000 period and find that a one percentage point drop in taxes increases per capita growth by 0.01 percentage points. Easterly and Rebelo (1993) also find that income taxes have a negative effect on growth. Since TFP is an important determinant of growth of an economy, the results of this paper are consistent with the results obtained in literature looking at the empirical effects of taxes on growth.

4

Model

In this section, I will build a simple DSGE model to explain the results of the empirical section. In this model workers accumulate human capital through hours of working. The mechanism used for skill accumulation is the same as used in Chang et al. (2002). The evolution of TFP depends on aggregate investment and human capital accumulated in the economy. It is assumed that there are a continuum of firms in the economy and since each firm is small, it ignores the effect of its own decisions on the level of productivity. Other 16 They also find that corporate taxes have a positive effect on TFP which is small but significant. However, they acknowledge that the positive effect of corporate taxes on labor productivity is counter intuitive and possibly results from a tax measure that does not adequately capture the changes in behavior of the firms 17 Distortionary taxes include taxes on income and profits.

13

main features of the model are convex capital adjustment costs and variable capital utilization. A positive personal or capital income tax shock reduces the amount of investment made by firms and human capital accumulation (by reducing the number of hours that workers work). This negative effect is then transmitted to TFP which in turn feeds back the negative effect into investment and human capital accumulation via wage rate and interest rate channels in future periods. Convex capital adjustment costs are required to control the drop in investment occurring because of this negative feed back from TFP.

4.1

Households

In the model economy, there is a large number of identical infinitely lived households. The representative consumer maximizes discounted utility defined over a stream of consumption and hours worked.

max

∞ X

β t U (Ct , Ht )

(2)

t=0

where U (Ct , Ht ) = θ

x1−σ H 1+z t − (1 − θ) t 1−σ 1+z

Ct is the consumption at time t. σ is a curvature parameter. Ht is the amount of time the consumer spends working. θ is the relative weight of the two components of utility. 0 < β < 1 is a discount factor. z is the inverse of Frisch elasticity of labor supply. The variable xt is a habit-adjusted consumption basket defined as xt = Ct − χCt−1

(3)

Following Chang et al. (2002), each worker has a skill18 level denoted by Xt . This represents the experience of the worker accumulated from past labor supplies. Skill of a worker increases the effective labor supplied by the worker. A worker with skill level Xt earns a wage that depends on both the market wage rate Wt∗ and his skill level. Wt (Xt ) = Wt∗ Xt The skill of a worker at time t depends on the amount of time spent working in the past.

ln(Xt ) = φln(Xt−1 ) + µln(Ht−1 ) 18 I

will also use the term ’human capital’ for the skill of a worker. They both refer to X.

14

(4)

The household owns the capital stock, Kt , and rents it to the firms at a rental rate Rt . The budget constraint faced by the representative household is given by  Ct + It + Ψ

It Kt

 Kt ≤ Wt (Xt )Ht (1 − τn,t ) + Rt (ut Kt )(1 − τk,t ) + T RAt

(5)

The left hand side of this equation shows the expenditures of household on consumption and investment in new capital. The right hand side shows the income of a household net of taxes. τn,t is the labor income tax rate. The term Wt (Xt )Ht denotes the total income earned from working, Wt (Xt )Ht (1 − τn,t ) shows the after tax labor income. Similarly, τk,t denotes the capital tax rate. ut is the rate of capital utilization and Rt (ut Kt )(1 − τk,t ) shows the after tax income from renting capital stock. T RAt denotes the lump sum   It transfers from government. Ψ K denotes the convex adjustment costs that the household must pay to t adjust it’s capital stock. The law of motion of capital is given by

Kt+1 = (1 − δ − g(ut ))Kt + It

(6)

where δ is the depreciation rate of capital and g(ut ) denotes the effect of variable capital utilization on the depreciation of capital stock.

4.2

Firms

There is a continuum of identical competitive firms that produce final goods according to a Cobb-Douglas technology using capital and effective units of labor.

Yt = At (ut Kt )α Nt1−α

(7)

Nt measures the number of units of effective labor supplied by the household. It includes both the number of hours worked, Ht , and the skill level of the worker, Xt .

Nt = Ht Xt

At represents the aggregate technology level of the economy. I assume that the each individual firm is small relative to the economy so its decisions do not affect the evolution of TFP. The evolution of TFP depends on the aggregate investment and human capital of the economy. The relationship between technology,

15

investment, and skill of workers can be be written in a recursive manner.

At+1 = f (At , It , Xt , et )

The above equation shows that technology depends both on its lagged value and the lagged values of investment and human capital accumulated by the workers. et is an exogenous shock to the technology process.19 et ∼ N (0, σe2 )

The functional form assumed in this model is similar to the one used for skill accumulation for workers.

At+1 = Aκt Itν Xtω eut

This specification is similar to the ones used in models of endogenous growth theory. In those models, there is a separate research and development sector that potentially uses the same inputs (labor, capital, human capital)as the final goods sector to produce ideas (technology) that goes into the production function of the final goods sector. In this model the population size has been normalized to 1 and there is no growth in population.20 Hence the level of technology only depends on investment made by firms and skill level of the workers. This production function for TFP is similar in nature to a number of functional forms previously considered in literature. Parente and Prescott (1994) consider evolution of technology through investment by the firm. Stadler (1990) consider a business cycle model in which technology evolves as a by product of aggregate production and is external to each individual firm. Romer (1990) consider a specification in which technology depends on human capital of workers involved in a research and development sector. Taking logs of both sides of the above equation

ln(At+1 ) = κln(At ) + νln(It ) + ωln(Xt ) + et 19 e t 20 If

(8)

is same across all firms. population grew at a constant rate n then the model would exhibit a balanced growth path in which TFP growth will be given by v(1 − α) gA = n (1 − α)(1 − κ) − ν

16

4.3

Government

The government collects taxes from households and them transfers them back to them in a lump sum fashion. It runs a balanced budget. Gt = T RAt = τn,t Wt (Xt )Ht + τk,t Rt ut Kt

4.4

(9)

Taxes

Labor and capital income taxes are governed by a stochastic process. I assume that taxes evolve according to an AR(1) process. I use the effective tax rates constructed in section 3.1.1 to estimate the persistence of the AR(1) processes for the taxes. McGrattan (1994) and Mertens and Ravn (2011) assume an AR(2) process for the tax evolution however using quarterly data on average tax rates, I find no support in favor of significance of the second lag for either tax process.

τn,t = (1 − η1 )τn + η1 τn,t−1 + n

(10)

τk,t = (1 − η2 )τk + η2 τk,t−1 + k

(11)

τn and τk are the long run steady state values of individual and capital tax rates. n and k represent the shocks to tax processes. The shocks are assumed to be i.i.d and uncorrelated.

 ∼ iid(0, Π )

where  = [n , k ] and Π is the variance covariance diagonal matrix of these shocks.

4.5

Equilibrium

I assume that the adjustment cost function for capital and the variable capital utilization function take the following forms.  Ψ

It Kt

 =

ψ 2



It −δ Kt

2

g(ut ) = Γuγt The following equations along with equations (4), (5), (6), (7), (8), (9), (10), (11) define the competitive equilibrium for the model. −σ λc,t = −(θ(x−σ )) t ) − βθχ(xt+1

17

(12)

   It 1+ψ −δ Kt      2   It+1 Yt+1 ψ It+1 It+1 = β (1 − τk,t+1 ) α − −δ +ψ −δ Kt+1 2 Kt+1 Kt+1 Kt+1     It+1 + 1+ψ −δ (1 − δ − uγt+1 ) Kt+1

λc,t λc,t+1

(13)

 1+z − λc,t (1 − α)Y (1 − τn,t ) = (1 − θ)Ht 1+z + −β φ(1 − θ)(Ht+1 ) + (φ − µ)(λc,t+1 (1 − α)Yt+1 (1 − τn,t+1 ))]

Γuγt

1 = .α(1 − τk,t ) γ

Wt∗ =



Yt Kt

(14)

 (15)

(1 − α)Yt Ht Xt

(16)

αYt ut Kt

(17)

Rt =

where λc,t is the multiplier on equation (5). Equation (12) sets this multiplier equal to the marginal utility of consumption which due to habit persistence depends on both current and future level of consumption.21 Equation (13) equates the shadow price of new capital to the present discounted value of marginal profits of having an extra unit of kt+1 .22 Equation(14) is the Euler equation for hours worked.23 This equation 21 It

is straight forward to check that setting χ = 0 eliminates habit formation from the model and equation (12) collapses to λc,t = −θc−σ t

which is the first order condition w.r.t. consumption in a standard model. 22 The first order condition w.r.t. investment yields    It λk,t = λc,t 1 + Ψ0 Kt where λk,t is the multiplier on equation (6). Defining qt =

λk,t λc,t

as the shadow value of an extra unit of capital in consumption

units, equation (13) can be rewritten as qt

=

    2 λc,t+1 Yt+1 ψ It+1 β (1 − τk,t+1 ) α − −δ λc,t Kt+1 2 Kt+1     It+1 It+1 +ψ −δ + qt+1 (1 − δ − Γuγt+1 ) Kt+1 Kt+1

(18)

23 Since hours worked today affects the skill level tomorrow, the equation is not static like in standard RBC models and involves intertemporal substitutions between hours worked. In absence of any skill accumulation, the terms with t + 1 subscript disappear and the same equation as in RBC models is obtained.

18

equates the marginal disutility of working to the marginal utility of consuming the labor share of income. Equation (15) defines the optimal utilization rate of capital as a function of its net rate of return. Equations (16) and (17) follow from firm’s maximization problem.

4.6

Model Estimation

The set of model parameters can be separated into two subsets Θ1 and Θ2 . Θ1 consists of parameters which can be easily calibrated. One time period in the model corresponds to one quarter. The discount factor β is set to 0.9926 which corresponds to a 3 percent annual real rate of interest. θ which is the weight of consumption in utility function is set equal to 0.5 so that the utility function assigns equal weights to consumption and labor. The depreciation rate δ is set equal to 0.025 which implies a 10 percent annual depreciation rate. The steady state values of income and capital tax rates, τn and τk , are set equal to 0.13 and 0.34 respectively which are the average values of these tax rates from the average tax series calculated in section 3.1.1 above. η1 which is the persistence parameter of the labor income tax process is set equal to 0.98, a number that is obtained by estimating an autoregressive process for the average labor tax rates. Similarly the value for η2 comes out to be 0.97. These parameters indicate high persistence for the tax processes. Table (2) gives a summary of calibrated parameters.

Θ2 consists of model parameters that have to be estimated.

Θ2 = [σ, z, φ, µ, κ, υ, ω, ψ, γ, χ, α]

Θ2 is estimated by matching the empirical impulse responses from section 3 with model-generated impulse responses. For this, I use the simulation estimation technique used by Cogley and Nason (1995). The parameters in Θ2 are estimated as those that solve the following problem

ˆ 2 = arg min[(Λ ˆ d − Λm (Θ2 |Θ1 ))0 Θ T T Θ2

−1 X

ˆ d − Λm (Θ2 |Θ1 ))] (Λ T T

(19)

d

ΛˆdT represents a column vector of empirical responses from section 2. Λm T (Θ2 |Θ1 )) represents the theoP−1 retical impulse responses from the model in which the set of calibrated parameters is taken as given. d is a weighting matrix. This is a diagonal matrix in which the estimates of variances of empirical response appear on the diagonal.

Some key parameters of the models need to be restricted so that their values lie within ranges consid-

19

ered plausible by the literature. These include the parameters governing the skill accumulation process and the evolution of TFP. The parameter µ which represents the elasticity of skill with respect to hours worked has been estimated in both micro and macro studies. Altug and Miller (1998) use PSID data for women to estimate that a 1 percent increase in annual hours leads to a 0.2 percent increase in the wage. Assuming that this increase in wage results from equal increases in each quarter, the quarterly elasticity would be around 0.05. Jacobson et al. (1993) find that annual wage loses of between 10 and 25 percent occur in the first year following the separation of worker from his job. This number converted to a quarterly frequency implies a value between 0.025 and 0.0625 for the elasticity µ. Chang et al. (2002) consider learning by doing in a business cycle framework. They employ a Bayesian approach that uses both micro-level PSID data on wages and hours and macro-level data on output growth and aggregate hours to estimate the parameters of the skill accumulation equation.24 The point estimate of φ in their paper is 0.7973 and the point estimate of µ is 0.1106. Based on these studies, I restrict φ to be close to 0.8 and µ to be between 0 and 0.09. I choose 0.09 because this value is in the middle of the range of values found in literature.

Choosing parameters for the evolution of TFP is less straightforward. There are no readily available estimates for the parameters used in equation (8). I first focus on the TFP of elasticity of experience represented by ω. The idea of learning by doing was first conceived by the Swedish economist Lundberg (1961) in his book Produktivitet och rantabilitet (Productivity and Profitability) and by Arrow (1962).25 More recently, the idea of experience curve effect (also called the learning curve effect) started to receive attention from empiricists. The experience curve effect states that the more often a task is performed, the lower the cost of doing it. This idea has been applied in various fields outside economics.26 The experience curve effect is usually summarized by the following functional form CN = N −ρ C1 where CN is the cost of producing N th unit, C1 is the cost of producing first unit and N is the aggregate 24 As

mentioned earlier, equation (4) used in this paper to represent learning by doing is borrowed from their paper. observed that the Horndal iron works of Fagersta, Sweden saw no new investments in physical capital (except for minimal repairs) between 1927 and 1952. Yet, the iron works experienced a production growth per hour of 2 percent annually. Lundberg called this “Horndal effect” as a pure productivity effect. Arrow (1962) attributed the Horndal effect to learning by doing. Paul David used the same idea to study the production growth in a cotton textile mill in Lawrence, Massachusetts between 1834 and 1856. He also observed that during this period the production of that mill grew by 2 percent per annum despite the absence of any investment in new machinery. He like Arrow (1962) attributed this increase in production to learning by doing of workers. However, these instances can merely be used as evidences in favor of human capital and experience affecting productivity evolution. The numerical values cannot be directly used because as Lundberg himself, and later Lazonick and Brush (1985), noted that this growth can be because of the increase in productivity resulting from accumulating experience but it can also result from changes in several undefined factors other than experience and physical capital. 26 See Harashima (2009) for a brief summary of papers outside economics with applications of learning curve effect. 25 Lundberg

20

volume of output which represents the experience of the worker involved in producing the units.27 ρ is called the learning rate. Boston Consulting Group (1970) estimate this learning rate to be between 0.15 and 0.42. Dutton and Thomas (1984) report the learning rates of a sample of 108 manufacturing firms. The values lie between 0.15 and 0.52 with an average of 0.29. These numbers imply that the cost of producing reduces by up to 30 percent when experience doubles. Assuming that the cost reduction comes entirely through productivity increase, this implies a TFP elasticity of experience of between 0.15 and 0.3. However, these estimations are done at individual firm level and are most likely to ignore any aggregate spill over effects across firms that may arise due to increase in experience of workers at firms. Thus, these values would then underestimate the true effect of experience on TFP.

I then turn to macroeconomic literature dealing with determinants of TFP. Islam (2008) uses the TFP index developed by Hall and Jones (1999) to perform a cross country analysis of the determinants of TFP. He finds that human capital is an important determinant of TFP. However the estimates presented in his study cannot be directly used here since they do not represent the elasticities. I use the human capital indexes used in Islam (1995) to look at their effect on the TFP indexes developed by Islam (1995) and Hall and Jones (1999).28 The estimated elasticities of TFP with respect to human capital range between 0.54 and 0.88. As expected, these values are higher than the estimates of learning rates presented earlier because these estimates include the aggregate effects of learning and human capital formation. Based on these studies, I choose a value of 0.75 for the TFP elasticity of experience that lies within the range of macro estimates and is higher than the micro estimates.

Next I look at the elasticity of TFP with respect to investment in physical capital. To estimate this value, I regress the baseline TFP measure on lagged values of investment and wages (which can also be viewed as a proxy for experience). The estimated TFP elasticity of investment is 0.033 and that with respect to wages is 0.72 (which is very close to the value chosen as the TFP elasticity of experience). The value that I choose for the TFP elasticity of investment is 0.04.

Finally, note that changes in both experience or investment will affect TFP beyond the first period. This results from the autoregressive component of TFP, coefficient of which is given by κ. A one percent rise in experience will increase TFP by ω percent in the first period but it will also change TFP by κω in the second 27 N takes discrete numerical values, N = {1, 2, 3, ...} where N = 2 refers to doubling of output and N = 3 refers to tripling of output and so on. 28 The human capital measures used in these papers are the average years of schooling for population aged 15 and above. These come from Mankiw et al. (1992) and Barro and Lee (1993). I regress the log of TFP indexes developed in Hall and Jones (1999) and Islam (1995) on the log of human capital indexes to come up with the estimated elasticities.

21

period and so on. Therefore the effective long run elasticity of TFP with respect to experience is given by ω 1−κ

and the elasticity with respect to investment is given by

ν 1−κ .

Thus these effective elasticities are set

equal to the values chosen above.29

To summarize, I restrict φ to be between 0 and 0.8, µ to be between 0 and 0.09, 0.04, and

4.7

ω 1−κ

ν 1−κ

to be equal to

to be equal to 0.75.

Benchmark Model

The first column of table (3) reports the parameter estimates for this model. σ is 1.1233 which is within the range of values considered plausible. z which is the inverse of labor supply elasticity is 0.5004 which is in line with values assumed in macroeconomic literature while lower than the values estimated in microeconomic literature.30 The point estimate of γ is 3.1056 which implies that variations in utilization of capital has a sizeable effect on it’s depreciation. ψ, which is the cost adjustment parameter of capital is 25.156. This number is slightly lower than the estimate of Ireland (2003) who finds this value to be 32.1346. Finally, the estimate of χ which is the habit persistence parameter is 0.6350. This value is very close to the value estimated by Christiano et al. (2005) (0.63). The value of φ is 0.7977 which is close to the value estimated by Chang et al. (2002) and the value of µ is 0.0898. The value of κ is 0.8085, ω is 0.1436, and ν is 0.0077.31

Figure (17) shows the results of simulations from this model. Since shocks to both types of taxes are assumed to be independent, the response of variables to total tax shock will be the sum of responses to individual shocks to labor income and capital taxes.32 The first plot shows the response of TFP to one percent rise in tax to GDP ratio from the model. The plot shows that while the model generated response of TFP to the tax shock shows a permanent decline similar to what is observed in the empirical response, it falls short of quantitatively matching its empirical counterpart. The model generated response remains outside the one standard error band for most of the quarters. The long run response of TFP implied by the model is about 4 times less than the empirical response of TFP. 29 This

gives us a system of two equations in three unknowns namely κ, ν, and ω. ν = 0.04 1−κ ω = 0.75 1−κ Without any extra information, it is not possible to identify them separately and for this reason the three parameters are allowed to vary freely while restricting them to satisfy the above two restrictions. 30 To have a larger labor supply elasticity in macro models than what micro estimates suggest is normal in the literature. See Chang and Kim (2006). 31 Recall that these parameters had restrictions imposed on them which are described in the previous subsection. 32 Both types of taxes increase by 1 percentage point which implies a one percentage point rise in tax revenue to GDP ratio. This ensures that the tax shock in the model and in the empirical exercise done earlier are comparable.

22

The second panel shows that the model is able to match the empirical response of investment in the short and long run, however, it fails to capture the decline in investment in the middle. The third panel shows that the output response marginally remains within the one standard error band of the empirical response but numerically it is still far from the point estimates. Other figures show that hours and consumption responses are well within the one standard error bands of their empirical counterparts although the hours response fails to match the shape of the empirically estimated response. Output per hour, like TFP, shows a similar trend as the response obtained from data but is numerically much smaller. The response of capital is also outside the one standard error band for most of the quarters.

Figures (18) and (19) shows the response of these variables to labor income and capital income tax shocks separately. Recall that the (responses to) total shock is the sum of (responses to) these two individual shocks. The results show that the model generated responses to labor income shock fall short of the empirical estimates. The response of TFP is again much smaller and outside the one standard error band of the estimated response though it does show the permanent decline that is observed in data as well. Figure (19) show that most of the variables show little movement in response to a shock to capital income tax. Thus the model is successful in producing the asymmetry observed between the responses to labor and capital income taxes in the data. The model is able to do this by having a higher TFP elasticity of experience relative to the TFP elasticity of investment. A positive shock to labor income tax reduces hours on impact. This reduction in hours persists for a long time because of the persistent nature of the shock. The decline in hours also reduces experience which then causes TFP to fall. This fall in TFP feeds back into the hours’ decision in the future periods via the wage channel. Similarly a positive shock to capital income tax reduces investment by affecting the rate of return on investment. This change also reduces TFP which then affects investment in subsequent periods by through the interest rate channel. However, as the elasticity of TFP elasticity of experience is higher, the feedback from TFP in subsequent periods is also higher which explains the differential effect of the two types of taxes in the model.

It must be emphasized that the results from the empirical exercises used to estimate the parameter values should be viewed with caution. In particular, the estimated numbers should be considered upper bounds on the parameters in questions rather than their true values. Indeed, regression of TFP on human capital alone omits some important variables.33 However, as Islam (2008) shows, the inclusion of such variables lowers the estimated elasticity of TFP with respect to human capital. This however, does not change the 33 See

Islam (2008) for a list of such variables.

23

main result of this section. Lower elasticity of TFP with respect to experience will further weaken the ability of the model to match the empirical responses. Thus by imposing upper bounds on values of key parameters of the modes, I am trying to give the model the best chance to match the data.

I defer the discussion about the gap between the model and empirical results to section (5). Next, I recalibrate the parameters of the model without subjecting them to the restrictions discussed in the previous subsection.

4.8

Model with freely chosen parameters

In this section, I recalibrate the model parameters to see whether the model is able to closely match the empirical responses when there are no restrictions on the key parameters of the model.34 The estimated parameters of this version of the model are in the second column of table (3). Looking at the first five rows of the table (which have the parameters of learning by doing and TFP evolution), it can be seen that the experience elasticity of hours and the TFP elasticity of hours are much higher in the model without any parameter restrictions. The persistence in TFP (κ) is almost the same in both models while the persistence in experience (φ) is lower in the model without restrictions.35 Finally, the elasticity of TFP with respect to investment is lower in the model with restrictions. Thus these estimates show that to match the data better, the model requires to have higher elasticities of experience and TFP with respect to hours and experience respectively.

The simulations results from the model without restrictions are given in figures (20)-(22). These figures show that this the model is quite successful in matching the main features of the empirical responses. The response of TFP to total ta shock is now much bigger in magnitude and closer to the estimates obtained from the data. The model generated response of investment again fails to match the drop observed in its empirical counterpart after about 6 quarters. Nonetheless, qualitatively, the model generated response matches the U shape of response from data. Output, output per hour, and consumption all closely match the empirical estimates. One failure of the model is its inability to generate the hours response that matches the response of hours from data. However, the model generates responses of hours that are within the confidence intervals of empirical responses. 34 Recall that the parameters of learning by doing (equation (4)) and TFP evolution (equation (8)) were restricted within certain ranges. In this section those parameters are allowed to vary freely. 35 The effective elasticity of experience given by φ is lower in the model with restrictions. 1−µ

24

5

Discussion

Previous section showed that the model where the parameter values were chosen based on previous studies failed to quantitatively match the empirical responses. There can be several reasons for the gap between the results from the model and data. Next, I briefly discuss these possibilities. 1. It is possible that the empirical results are overstating the true effects of tax changes on TFP. The way Romer and Romer (2009) construct their tax series gives rise to the possibility of some spurious results. The exogenous tax changes of Romer and Romer (2009) consist of those tax changes that were either taken to reduce inherited debt or to affect long run growth. Consider the tax changes that were taken in response to concerns about inherited debt. Fiscal authorities would raise taxes to eliminated long run debt if they do not anticipate normal growth of the economy to be enough to deal with the debt.36 Since TFP is an important part of growth, this will show up as a negative correlation between taxes and TFP which will bias the results upwards. If these concerns are real then we would expect to see an inflated response of TFP to Romer and Romer (2009) tax measures. 2. The gap between the impulse responses generated by the model and empirical responses may also arise due to the model not being rich enough. It is not obvious what, if any, channels are missing in the model. The model derives its components from both the business cycle and endogenous growth literature. In endogenous growth models, TFP evolves through investments in physical and human capital. The model presented in this paper includes both these channels, albeit in a reduced form manner that allows for business cycle fluctuations to be treated in a tractable way. Thus this shows that the existing literature, while being successful at explaining observed moments at business cycle frequencies, are incapable in accounting for data patterns at the longer horizons. 3. Finally, the gap between the model generated results and the results implied by the data may be due to the parameter values used. The last section showed that once the parameter values are chosen freely, the model is able to match the data quite well. Thus it may be the case that the parameter estimates implied by micro studies are different from those used in macro models. Such tension between micro studies is neither new nor unknown.37

Of the five key parameters used in the model presented in this paper, it is unlikely that the val36 It may be argued that such tax changes do not necessarily represent the beliefs of administration about growth of output, rather they may just result from different preferences regarding long run debt of a new administration. 37 The most well known case of a difference between micro and macro estimates of a particular parameter is that of labor supply elasticity. The estimates of labor supply elasticity from micro studies are significantly lower than the estimates used in macro models.

25

ues used for the parameters of TFP evolution equation (equation (8)) are too far from their true values since the chosen parameter values were based on macro estimations and studies. Table (3) shows that in order to match the responses generated by the data, the effective TFP elasticity should be around 4.15 which is more than 5 times the values observed in different studies. Thus it is highly unlikely to have such a high TFP elasticity of experience.

The value of µ, elasticity of experience with respect to hours worked, on the other hand is based on micro studies. It is possible that these micro studies fail to capture the spill over effects from the increase in hours of other workers that would affect the experience of a worker. I re-estimated the model by allowing µ to vary freely but kept the other restrictions in place. The results show that a higher value of µ is indeed enough to get the model generated responses closer to those from data. However, for this, µ needs to be in excess of 0.7 or nearly 9 times the values that was chosen based on previous literature. Even if the micro studies underestimate the true value of elasticity of experience with respect to hours by ignoring any spill over effects, it is highly unlikely that the size of underestimation is this big. Thus, the gap between the model-generated and empirical results cannot entirely be due to calibration issues.

6

Conclusion

This paper used the Romer and Romer (2009) data on tax shocks to estimate its response on utilization adjusted TFP as measured by Fernald (2009). Only the permanent, exogenous tax shocks were considered in the baseline case. The results of a 3 variable VAR that included the tax measure, log of output and log of TFP showed two key findings, 1) TFP responds strongly and negatively to tax changes in the long run, and this change in TFP represents about 80 percent of the change that occurs in real output following the tax change. And 2) even in the short run, changes in TFP account for about one third of the response of output. The results further show that only labor income taxes have a significant effect on most of the variables, capital taxes don’t have any significant effect.

I then built a DSGE model which had learning by doing at the worker level and endogenous TFP evolution that depended on investment and human capital. The results show that for carefully chosen parameter values, the model fails to match the empirical responses of TFP and other variables to tax shocks. However, for freely chosen parameters, the model is able to closely match the empirical responses. I argue that the gap between model and empirical results can be due to data overstating the results, the model missing some

26

key channels, parameter values being underestimated in micro studies or a combinations of these. In future, it will be interesting to pursue each of these possibilities in detail to come up with a possible reconciliation between the data and model.

27

References Acemoglu, D., Introduction to Modern Economic Growth (Princeton University Press, 2008). Altug, S. and R. A. Miller, “The Effect of Work Experience on Female Wages and Labour Supply,” Review of Economic Studies 65 (January 1998), 45–85. Arnold, J. and C. Schwellnus, “Do Corporate Taxes Reduce Productivity and Investment at the Firm Level? Cross-Country Evidence from the Amadeus Dataset,” Working Papers 2008-19, CEPII research center, September 2008. Arrow, K. J., “The Economic Implications of Learning by Doing,” The Review of Economic Studies 29 (1962), pp. 155–173. Barro, R. J. and J.-W. Lee, “International comparisons of educational attainment,” Journal of Monetary Economics 32 (December 1993), 363–394. Barro, R. J. and C. J. Redlick, “Macroeconomic Effects from Government Purchases and Taxes,” NBER Working Papers 15369, National Bureau of Economic Research, Inc, September 2009. Basu, S., J. G. Fernald and M. S. Kimball, “Are Technology Improvements Contractionary?,” The American Economic Review 96 (2006), pp. 1418–1448. Bils, M. and J.-O. Cho, “Cyclical factor utilization,” Journal of Monetary Economics 33 (1994), 319 – 354. Blanchard, O. and R. Perotti, “An Empirical Characterization Of The Dynamic Effects Of Changes In Government Spending And Taxes On Output,” The Quarterly Journal of Economics 117 (November 2002), 1329–1368. Blankenau, W. F., “Public Education Expenditures, Taxation, and Growth: Linking Data to Theory,” American Economic Review 97 (2007), 393–397. Boston Consulting Group, Perspectives on experience (The Boston Consulting Group, 1970). Chang, Y., J. F. Gomes and F. Schorfheide, “Learning-by-Doing as a Propagation Mechanism,” The American Economic Review 92 (2002), pp. 1498–1520. Chang, Y. and S.-B. Kim, “From Individual To Aggregate Labor Supply: A Quantitative Analysis Based On A Heterogeneous Agent Macroeconomy,” International Economic Review 47 (02 2006), 1–27.

28

Christiano, L. J., M. Eichenbaum and C. L. Evans, “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy,” Journal of Political Economy 113 (February 2005), 1–45. Cogley, T. and J. M. Nason, “Output Dynamics in Real-Business-Cycle Models,” American Economic Review 85 (June 1995), 492–511. Dutton, J. M. and A. Thomas, “Treating Progress Functions as a Managerial Opportunity,” The Academy of Management Review 9 (1984), pp. 235–247. Easterly, W. and S. Rebelo, “Fiscal policy and economic growth,” Journal of Monetary Economics 32 (1993), 417 – 458. Fernald, J., “A Quartely Utilization-Adjusted Series on Total Factor Productivity,” Manuscript (2009), available at http://www.frbsf.org/economics/economists/jfernald/Quarterly-TFP.pdf, 2009. Gemmel, N., R. Kneller, I. Sanz and J. F. Sanz-Sanz, “Corporate Taxation and the Productivity and Investment Performance of Heterogeneous Firms: Evidence from OECD Firm-Level Data,” preprint (2010), available at http://ftp.zew.de/pub/zew-docs/veranstaltungen/Draft Kneller.pdf, 2010. Hall, R. E. and C. I. Jones, “Why Do Some Countries Produce So Much More Output Per Worker Than Others?,” The Quarterly Journal of Economics 114 (February 1999), 83–116. Harashima, T., “A Theory of Total Factor Productivity and the Convergence Hypothesis: Workers Innovations as an Essential Element,” MPRA Paper 15508, University Library of Munich, Germany, May 2009. Heylen, F. and R. Schoonackers, “Fiscal Policy and TFP in the OECD: A Non-Stationary Panel Approach,” Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 11/701, Ghent University, Faculty of Economics and Business Administration, January 2011. Ireland, P. N., “Endogenous money or sticky prices?,” Journal of Monetary Economics 50 (2003), 1623 – 1648. Islam, N., “Growth Empirics: A Panel Data Approach,” The Quarterly Journal of Economics 110 (November 1995), 1127–70. ———, “Determinants of Productivity Across Countries: An Exploratory Analysis,” The Journal of Developing Areas 42 (2008), 1127–70. Jacobson, L. S., R. J. LaLonde and D. G. Sullivan, “Earnings Losses of Displaced Workers,” The American Economic Review 83 (1993), pp. 685–709. 29

Kim, S.-J., “Growth effect of taxes in an endogenous growth model: to what extent do taxes affect economic growth?,” Journal of Economic Dynamics and Control 23 (1998), 125 – 158. Kneller, R., M. F. Bleaney and N. Gemmell, “Fiscal policy and growth: evidence from OECD countries,” Journal of Public Economics 74 (1999), 171 – 190. Kydland, F. E. and E. C. Prescott, “Time to Build and Aggregate Fluctuations,” Econometrica 50 (November 1982), 1345–70. Lazonick, W. and T. Brush, “The horndal effect in early U.S. manufacturing,” Explorations in Economic History 22 (1985), 53–96. Long, J., John B. and C. I. Plosser, “Real Business Cycles,” Journal of Political Economy 91 (1983), pp. 39–69. Lucas, R. J., “On the mechanics of economic development,” Journal of Monetary Economics 22 (July 1988), 3–42. Lundberg, E., Produktivitet och r¨ antabilitet:

studier i kapitalets betydelse inom svenskt n¨ aringsliv

(Studief¨ orbundet N¨ aringsliv och samh¨ alle, 1961). Mankiw, N. G., D. Romer and D. N. Weil, “A Contribution to the Empirics of Economic Growth,” The Quarterly Journal of Economics 107 (1992), pp. 407–437. McGrattan, E. R., “The macroeconomic effects of distortionary taxation,” Journal of Monetary Economics 33 (1994), 573 – 601. Mendoza, E. G., A. Razin and L. L. Tesar, “Effective tax rates in macroeconomics: Cross-country estimates of tax rates on factor incomes and consumption,” Journal of Monetary Economics 34 (1994), 297 – 323. Mertens, K. and M. O. Ravn, “Understanding the Aggregate Effects of Anticipated and Unanticipated Tax Policy Shocks,” Review of Economic Dynamics 14 (January 2011), 27–54. Parente, S. L. and E. C. Prescott, “Barriers to Technology Adoption and Development,” Journal of Political Economy 102 (April 1994), 298–321. Ribeiro, M. J., “Endogenous Growth: Analytical Review of its Generating Mechanisms,” Technical Report, 2003.

30

Romer, C. and D. Romer, “A Narrative Analysis of Postwar Tax Changes,” Not Intended for Publication (2009), available at http://elsa.berkeley.edu/ dromer/papers/nadraft609.pdf, 2009. ———, “The Macroeconomic Effects of Tax Changes: Estimates Based on a New Measure of Fiscal Shocks,” American Economic Review 100 (June 2010), 763–801. Romer, P. M., “Endogenous Technological Change,” Journal of Political Economy 98 (October 1990), S71–102. Schor, J., Does work intensity respond to macroeconomic variables?: evidence from British manufacturing, 1970-1986, Discussion paper (Harvard Institute of Economic Research, Harvard University, 1988). Stadler, G. W., “Business Cycle Models with Endogenous Technology,” The American Economic Review 80 (1990), pp. 763–778.

31

Figure 1. Measure of Tax Shocks.

32

Figure 2. Response of purified TFP to changes (permanent, exogenous) in taxes.

Figure 3. Response of TFP(bold) and Output to changes (permanent, exogenous) in taxes.

Figure 4. Response of purified TFP to changes (permanent, exogenous and endogenous) in taxes. (Response to exogenous only also plotted, response to endogenous and exogenous combined in bold)

33

Figure 5. Response of purified TFP to changes (average in taxes. (Response to exogenous only also plotted, response to average taxes in bold)

marginal )

Figure 6. Response of Unadjusted TFP to changes (permanent, in taxes. (Response of purified tfp also plotted, response of unadjusted TFP in bold)

exogenous)

Figure 7. Response of Bils and Cho (1994) measure of TFP to changes (permanent, exogenous) in taxes. (Response of purified tfp also plotted, response of BC measure of TFP in bold)

Figure 8. Response of Purified TFP to changes in taxes estimated separately for pre and post 1980 periods. post 1980 in bold)

34

(permanent, exogenous) (Response of purified TFP for

Figure 9. Response of output to changes (permanent, exogenous) in taxes

.

Figure 10. Response of gross private investment to changes (permanent, exogenous) in taxes

.

Figure 11. Response of capital to changes (permanent, exogenous) in taxes

.

35

Figure 12. Response of average hours to changes (permanent, exogenous) in taxes

.

Figure 13. Response of employment to changes (permanent, exogenous) in taxes

.

Figure 14. Response of output per hour to changes (permanent, exogenous) in taxes

.

36

Figure 15. Response of real wage to changes (permanent, exogenous) in taxes

.

Figure 16. Response of private consumption to changes (permanent, exogenous) in taxes

.

37

Figure 17. Impulse responses to shock to total tax from the benchmark model.

38

Figure 18. Impulse responses to shock to labor income tax from the benchmark model.

39

Figure 19. Impulse responses to shock to capital tax from the benchmark model.

40

Figure 20. Impulse responses to shock to total tax from the model with freely chosen parameters.

41

Figure 21. Impulse responses to shock to labor income tax from the model with freely chosen parameters.

42

Figure 22. Impulse responses to shock to capital tax from the model with freely chosen parameters.

43

Variable

Source

Output Investment Consumption Average Hours Employment Output per hour Real Wage Population Total Factor Productivity Total tax shocks Individual and Corporate tax shocks

Bureau of Economic Analysis Bureau of Economic Analysis Bureau of Economic Analysis Bureau of Labor Statistics Bureau of Labor Statistics Bureau of Labor Statistics Bureau of Labor Statistics Bureau of Labor Statistics Fernald (2009) Romer and Romer (2009) Constructed using Romer and Romer (2009) sources.

Table 1. Data definitions and sources

44

45

Interpretation

Discount Factor Steady state individual income rate rate Steady state capital income tax rate Weight of consumption in utility function Depreciation

Parameter

β τn τk θ δ

3 % annual interest rate Average of average marginal income taxes Average of average marginal corporate taxes Equal weights of consumptions and leisure. 10 percent annual depreciation

Source

Table 2. Calibrated Parameters

0.9926 0.13 0.34 0.5 0.025

Value

Parameter

φ µ κ ν ω z α ψ γ Γ χ σ θ

Interpretation

Model-Parameters Restricted

Model-Free Parameters

Persistence in X Elasticity of X w.r.t. H Persistence in A Elasticity of A w.r.t. I Elasticity of A w.r.t. X Labor supply elasticity Share of capital Cost parameter Utilization parameter Utilization parameter Habit parameter Curvature parameter Preference Parameters

0.7977 0.0898 0.8085 0.0077 0.1436 0.5004 0.3001 25.156 3.1056 0.8294 0.6350 1.1233 0.7362

0.7352 0.1998 0.8005 0.0027 0.8461 0.5035 0.3009 34.868 2.8258 0.9493 0.5645 1.2236 0.4037

Obj. Func.

397.145

251.670

Table 3

46